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nonlinear system nonlinear let u0 be a nominal input

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Unformatted text preview: ont.) Nonlinear system: Nonlinear Let u0 be a nominal input and let the resultant Let state be x0 Perturbation: Perturbation: Resultant perturb: Resultant Taylor series expansion: Taylor notice that N. sys 7 ; hence L. sys. 8 Linearization of a pendulum model Motion of the pendulum Motion Linearization of a pendulum model (cont’) Taylor series expansion of Taylor Linearize it at Linearize Find u0 Find New coordinates: New 9 Time delay transfer function 10 Summary and Exercises TF derivation TF Modeling of Modeling Nonlinear systems Nonlinear Systems with time delay Systems Next Next (Memorize this!) Modeling of DC motors Modeling Exercises Exercises The more time delay is, the more difficult to The control (Imagine that you are controlling the temperature of your shower with a very long hose. You will either get burned or frozen!) Linearize the pendulum model at π/4 Linearize 11 12...
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